Active laser medium: Difference between revisions
en>Shawn Worthington Laser Plasma List of laser articles added |
en>Nanite |
||
Line 1: | Line 1: | ||
{{no footnotes|date=February 2013}} | |||
[[File:Ulaw alaw db.svg|thumb|350px|Graph of μ-law & A-law algorithms]] | |||
An '''A-law algorithm''' is a standard [[companding]] algorithm, used in [[Europe]]an [[Digital data|digital]] [[Telecommunication|communications]] systems to optimize, ''i.e.,'' modify, the [[dynamic range]] of an [[analog signal]] for digitizing. | |||
It is similar to the [[μ-law algorithm]] used in [[North America]] and [[Japan]]. | |||
For a given input ''x'', the equation for A-law encoding is as follows, | |||
:<math> | |||
F(x) = \sgn(x) \begin{cases} {A |x| \over 1 + \ln(A)}, & |x| < {1 \over A} \\ | |||
\frac{1+ \ln(A |x|)}{1 + \ln(A)}, & {1 \over A} \leq |x| \leq 1, \end{cases} | |||
</math> | |||
where ''A'' is the compression parameter. In Europe, <math>A = 87.7</math>; the value 87.6 is also used. | |||
A-law expansion is given by the inverse function, | |||
:<math> | |||
F^{-1}(y) = \sgn(y) \begin{cases} {|y| (1 + \ln(A)) \over A}, & |y| < {1 \over 1 + \ln(A)} \\ | |||
{\exp(|y| (1 + \ln(A)) - 1) \over A}, & {1 \over 1 + \ln(A)} \leq |y| < 1. \end{cases} | |||
</math> | |||
The reason for this encoding is that the wide [[dynamic range]] of [[Speech communication|speech]] does not lend itself well to efficient linear digital encoding. A-law encoding effectively reduces the dynamic range of the signal, thereby increasing the [[Channel coding|coding]] efficiency and resulting in a signal-to-[[distortion]] ratio that is superior to that obtained by linear encoding for a given number of bits. | |||
== Comparison to μ-law == | |||
The [[μ-law algorithm]] provides a slightly larger dynamic range than the A-law at the cost of worse proportional distortion for small signals. By convention, A-law is used for an international connection if at least one country uses it. | |||
== See also == | |||
* [[μ-law algorithm]] | |||
* [[Audio level compression]] | |||
* [[Signal compression]] | |||
* [[Companding]] | |||
* [[G.711]] | |||
* [[DS0]] | |||
== External links == | |||
* [http://www.cisco.com/en/US/tech/tk1077/technologies_tech_note09186a00801149b3.shtml Waveform Coding Techniques] - Has details of implementation (but note that the A-law equation is incorrect) | |||
* [http://www.eettaiwan.com/ARTICLES/2001MAY/PDF1/2001MAY02_NTEK_DSP_AN1135.PDF A-Law and μ-law Companding Implementations Using the TMS320C54x] ([[PDF]]) | |||
* [https://github.com/deftio/companders A-law implementation in C-language with example code] | |||
{{Compression Methods}} | |||
[[Category:Audio codecs]] |
Revision as of 22:45, 20 January 2014
An A-law algorithm is a standard companding algorithm, used in European digital communications systems to optimize, i.e., modify, the dynamic range of an analog signal for digitizing.
It is similar to the μ-law algorithm used in North America and Japan.
For a given input x, the equation for A-law encoding is as follows,
where A is the compression parameter. In Europe, ; the value 87.6 is also used.
A-law expansion is given by the inverse function,
The reason for this encoding is that the wide dynamic range of speech does not lend itself well to efficient linear digital encoding. A-law encoding effectively reduces the dynamic range of the signal, thereby increasing the coding efficiency and resulting in a signal-to-distortion ratio that is superior to that obtained by linear encoding for a given number of bits.
Comparison to μ-law
The μ-law algorithm provides a slightly larger dynamic range than the A-law at the cost of worse proportional distortion for small signals. By convention, A-law is used for an international connection if at least one country uses it.
See also
External links
- Waveform Coding Techniques - Has details of implementation (but note that the A-law equation is incorrect)
- A-Law and μ-law Companding Implementations Using the TMS320C54x (PDF)
- A-law implementation in C-language with example code